Refuting misconceptions: Computer tutors for fraction arithmetic

Fractions, known to be difficult for both children and adults, are especially prone to misconceptions and erroneous strategy selection. The present study investigated whether a computer tutor improves fraction arithmetic performance in adults and if supplementing problem solving with erroneous examples is more beneficial than problem solving alone. Seventy-five undergraduates solved fraction arithmetic problems using a computer tutoring system we designed. In a between-subjects design, 39 participants worked with a problem-solving tutor that was supplemented with erroneous examples and 36 participants worked with a traditional problem-solving tutor. Both tutors provided hints and feedback. Overall, participants improved after the tutoring interventions, but there were no significant differences in gains made by the two conditions. For students with low prior knowledge about fraction arithmetic, the numerical gains were higher in the erroneous-example group than the problem-solving group, but this effect was not significant. Thus, computer tutors are useful tools for improving fraction knowledge. While erroneous examples may be particularly beneficial for students with low prior knowledge who may hold more misconceptions, more research is needed to make this conclusion.

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The Effects of Context-based Problem-solving Tasks on Students’ Interest and Metacognitive Experiences

Open Education Studies ◽

10.1515/edu-2020-0118 ◽

2020 ◽

Vol 2 (1) ◽

pp. 112-125

Author(s):

Marcela Pozas ◽

Patrick Löffler ◽

Wolfgang Schnotz ◽

Alexander Kauertz

Keyword(s):

Problem Solving ◽

Prior Knowledge ◽

Situational Interest ◽

Analysis Of Covariance ◽

Task Characteristics ◽

Factor Analyses ◽

Subject Factor ◽

Problem Solving Process ◽

High Track ◽

Metacognitive Experiences

AbstractPrior knowledge, motivational factors, and metacognition have been long considered basic elements for successful problem-solving process. However, the interplay of these variables with context-based task characteristics has rarely been explored in research. The present study aimed at investigating how context-based task characteristics influence these three elements, and further expands to explore potential differentiated effects across physics’ topics. A multivariate analysis of covariance was conducted with 232 participants from high-track schools in Germany to investigate the effects of task characteristics and task topic with regard to their motivational and metacognitive variables. Overall results indicated that students’ situational interest and estimate of solution correctness decrease through time as a result from their interaction with the tasks characteristics. Furthermore, between-subject factor analyses revealed important differences across the task topics of mechanics and thermodynamics. Finally, the covariate of prior knowledge was positively significant across all analyses. The findings demonstrate the importance of appropriate design of context-based tasks to positively influence students’ motivation and metacognitive processing. Implications of the results, as well as further lines of research are discussed.

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THE INSTRUCTION TO OVERCOME THE INERT KNOWLEDGE ISSUE IN SOLVING MATHEMATICAL PROBLEM

Jurnal Gantang ◽

10.31629/jg.v1i1.2 ◽

2016 ◽

Vol 1 (1) ◽

pp. 16-25 ◽

Cited By ~ 1

Author(s):

Febrian Febrian

Keyword(s):

Mathematics Education ◽

Problem Solving ◽

Prior Knowledge ◽

Mathematical Problem ◽

Mathematical Problem Solving ◽

Realistic Mathematics Education ◽

Literature Study ◽

Realistic Mathematics ◽

Knowledge Access

One characteristic of typical mathematical problem is that it requires bunch of relevant prior knowledge. This knowledge is built consecutively and is recalled whenever needed to promote student to solve the problem. The process undertaken by the solver to utilize existing relevant prior knowledge while solving the problem is called access. However, this access is possible subject to disturbance for some reasons. This literature study addresses some factors that can distract access: factor related to metaprocess and factor related to deficit structure. The variants included in both factors have been proved through research as the contributors of the accessibility of relevant prior knowledge. Knowledge that cannot be accessed is called inert knowledge, the main reason for why solver face the difficulty to find the answer to given mathematical problem. The explanation leads to the suggestion of how to tackle the inertia of particular knowledge. One of them are through the instruction setting. Realistic Mathematics Education as one of approaches in learning can be a possible alternative for the issue of inert knowledge. Keywords. Mathematical problem solving, prior knowledge, access, inert knowledge, Realistic Mathematics Education

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